Educational Studies in Mathematics

, Volume 85, Issue 3, pp 381–403 | Cite as

Digital technologies to teach and learn mathematics: Context and re-contextualization



The central assumption of this paper is that, especially in the field of digital technologies to teach and learn mathematics, the influence of the context in which research is carried out has not been given enough attention, so that research results are not really useful outside this context. We base our discussion on the work of a group of European teams carrying out research with a special methodology of “cross-studies” and carrying out “cross-analyses” of particular studies. A context for a research study is described as a dynamic construction by researchers, connecting relevant contextual characteristics in the settings (empirical and academic) where research activity takes place and helping to gain insight from the outcomes of the study. Analyzing the design of two “Didactical Digital Artefacts,” and the associated cross-studies involving teams of three countries, we identify more or less conscious influences of characteristics in the researchers' contexts upon research outcomes. Cross-studies and cross-analysis help to go further by making researchers more aware of their context and of its characteristics. It also helps researchers to “re-contextualize,” that is to say to identify new contextual characteristics in the settings they are acting in, to gain insight from research outcomes that emerged in other contexts.


Digital technologies Cross-study Cross-analysis Context Empirical context Academic context Casyopée, Cruislet 


  1. Artigue, M. (coord.) (2009). Integrative Theoretical Framework–Version C. Deliverable 18, ReMath Project.
  2. Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematics Learning, 7(3), 245–274.Google Scholar
  3. Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (second revised edition (pp. 746–783). Mahwah: Lawrence Erlbaum.Google Scholar
  4. Bottino, R. M., & Kynigos, C. (2009). Mathematics education & digital technologies: Facing the challenge of networking European research teams. International Journal of Computers for Mathematical Learning, 14(3), 203–215.Google Scholar
  5. Brousseau, G. (1997). The theory of didactic situations in mathematics. Dordrecht: Kluwer.Google Scholar
  6. Cerulli, M., Trgalová, J., Marraci, M., Psycharis, G., & Georget, J.-P. (2008). Comparing theoretical frameworks enacted in experimental research: TELMA experience. Zentralblatt fur Didaktik der Mathematik, 40(2), 201–213.CrossRefGoogle Scholar
  7. Chevallard, Y. (1999). L'analyse des pratiques enseignantes en théorie anthropologique du didactique [Analysing teaching practices within the anthropologic theory of didactics]. Recherches en didactique des mathématiques, 19(2), 221–266.Google Scholar
  8. Cuoco, A. (2002). Thoughts on reading Artigue's “Learning mathematics in a CAS environment. International Journal of Computers for Mathematical Learning, 7(3), 293–299.CrossRefGoogle Scholar
  9. Gallou-Dumiel, E. (1987). Symétrie orthogonale et micro-ordinateur [Geometrical reflection and micro-computer]. Recherches en didactique des mathématiques, 8(1–2), 5–59.Google Scholar
  10. Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematics Learning, 3(3), 195–227.Google Scholar
  11. Healy, L., & Kynigos, C. (2010). Charting the microworld territory over time: Design and construction in learning, teaching and developing mathematics. ZDM, The International Journal of Mathematics Education, 42, 63–76.Google Scholar
  12. Jackiw, N. (2010). Attention to detail; Broadening our design language. In C. Hoyles & J. B. Lagrange (Eds.), Mathematics education and technology: Rethinking the terrain (pp. 431–433). New York: Springer.Google Scholar
  13. Kahane, J. (coord.) (2002) L'enseignement des sciences mathématiques [Teaching mathematical sciences]. Centre National de Documentation Pédagogique, Odile Jacob, Paris.Google Scholar
  14. Kieran, C. (2004). The Core of Algebra: Reflections on its main activities. In K. Stacey (Ed.), The future of teaching and learning of algebra: 12th ICMI Study (pp. 21–24). Dordrecht: Kluwer.CrossRefGoogle Scholar
  15. Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In: Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707–762). Greenwich, CT: Information Age Publishing.Google Scholar
  16. Kieran, C., & Drijvers, P. (2007). The Co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of cas use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11(2), 205–263.Google Scholar
  17. Kynigos, C., & Psycharis, G. (2009). The role of context in research involving the design and use of digital media for the learning of mathematics: Boundary objects as vehicles for integration. International Journal of Computers for Mathematical Learning, 14(3), 265–298.Google Scholar
  18. Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-geometry. International Journal of Computers for Mathematical Learning, 6, 283–317.CrossRefGoogle Scholar
  19. Lagrange, J. B. (1999). Complex calculators in the classroom: Theoretical and practical reflections on teaching precalculus. International Journal of Computers for Mathematical Learning, 4(1), 51–81.Google Scholar
  20. Lagrange, J. B. (2000). L'intégration d'instruments informatiques dans l'enseignement : Une approche par les techniques [Integrating computer tools into mathematics teaching: The role of "techniques"]. Educational Studies in Mathematics, 43(1), 1–30.Google Scholar
  21. Lagrange, J. B. (2013). Analyzing teacher classroom use of technology: Anthropological Approach and Activity Theory. International Journal for Technology in Mathematics Education, 20(1), 33–37.Google Scholar
  22. Lagrange, J.-B., & Artigue, M. (2009). Students' activities about functions at upper secondary level: A grid for designing a digital environment and analysing uses. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 465–472). Thessaloniki, Greece: PME.Google Scholar
  23. Lagrange, J.-B., Artigue M., Laborde C., & Trouche L. (2003). Technology and mathematics éducation: A multidimensional study of the evolution of research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & K. S. F. Leung (Eds.), Second international handbook of mathematics education, Part 1 (pp. 237–269). Dordrecht: Kluwer Academic Publishers.Google Scholar
  24. Le Feuvre, B., Meyrier, X., & Lagrange, J. B. (2010). Apprendre des notions mathématiques, géographiques et algorithmiques à l'aide d'un environnement de navigation 3D au-dessus de la Grèce [Learning mathematics, geography and algorithmics by way of a 3D virtual navigator over Greece]. Repères IREM, 81, 29–48.Google Scholar
  25. Lave, J. (1988). Cognition in practice. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  26. Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.Google Scholar
  27. Maracci, M., Cazes, C., Vandebrouck, F., & Mariotti, M. A. (2013). Synergies between theoretical approaches to mathematics education with technology: A case study through a cross-analysis methodology. Educational Studies in Mathematics, 84(3), 461–485.CrossRefGoogle Scholar
  28. Markopoulos, C., Kynigos, C., Alexopoulou, E., & Koukiou, A. (2009). Mathematisations while navigating with a geo-mathematical microworld. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 97–104). Thessaloniki, Greece: PME.Google Scholar
  29. Minh, T. K. (2012). Learning about functions with the help of technology: Students' instrumental genesis of a geometrical and symbolic environment. In T. Y. Tso (Ed.), Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 217–224). Taipei, Taiwan: PME.Google Scholar
  30. Monaghan, J. (2009). People and theories. Proceedings of CERME 6, January 28th-February 1st 2009, Lyon France © INRP 2010
  31. Monaghan, J. (2005). Computer algebra. Instrumentation and the anthropological approach. International Journal for Technology in Mathematics Education, 14(2), 63–71.Google Scholar
  32. Sriraman, B., & English, L. (Eds.). (2010). Theories of mathematics education: Seeking new frontiers. Berlin/Heidelberg: Springer Science.Google Scholar
  33. Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267–307). Hillsdale, NJ: Erlbaum.Google Scholar
  34. Tall, D. (1996). Functions and calculus. In A. J. Bishop et al. (Eds.), International handbook of mathematics education (pp. 289–325). Dordrecht: Kluwer.Google Scholar
  35. Van Oers, B. (1998). From context to contextualizing. Learning and Instruction, 8(6), 473–488.CrossRefGoogle Scholar
  36. Verillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 9(3), 77–101.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Laboratoire de Didadactique André RevuzUniversity Paris 7 DIDEROTParisFrance
  2. 2.University of ReimsReimsFrance
  3. 3.Educational Technology LabN.K. University of AthensAthensGreece

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